feat(sync): follow the visit sync on the dashboard

Show the "Syncing with Steam" badge while a visit sync runs, then
reload the sync changes banner and the library.

src/pages/Dashboard.visitSync.test.jsx

@@ -0,0 +1,64 @@
+// @vitest-environment jsdom
+import {afterEach, beforeEach, describe, expect, it, vi} from 'vitest';
+import {act, cleanup, screen} from '@testing-library/react';
+import Dashboard from './Dashboard.jsx';
+import {fetchRoutes, json} from '../test/fetchRoutes.js';
+import {renderWithProviders} from '../test/renderWithProviders.jsx';
+
+vi.mock('react-i18next', () => import('../test/i18n-mock.js'));
+
+const empty = {content: [], total: 0, byStatus: {}};
+const wait = (ms) => act(() => vi.advanceTimersByTimeAsync(ms));
+const calls = (path) => fetch.mock.calls.filter(([url]) => new URL(url, 'http://x').pathname.endsWith(path)).length;
+
+beforeEach(() => {
+    vi.useFakeTimers({shouldAdvanceTime: true});
+    localStorage.setItem('tbp_session', '1');
+});
+
+afterEach(() => {
+    cleanup();
+    vi.useRealTimers();
+    localStorage.clear();
+});
+
+describe('Dashboard sync on a visit', () => {
+    it('showsTheSyncingBadgeDuringTheVisitSyncAndReloadsBannerAndLibraryAfterIt', async () => {
+        let syncStatus = {lastSyncStatus: 'OK', lastSyncedAt: '2026-10-03T10:00:00Z'};
+        let syncChanges = json(204, {});
+        fetchRoutes({
+            'GET /api/library/summary': json(200, empty),
+            'GET /api/hints': json(200, {results: []}),
+            'GET /api/news': json(200, {results: []}),
+            'GET /api/library/sync-changes': () => syncChanges,
+            'GET /api/users/me': json(200, {email: 'a@b.de', displayName: 'Lobo', steamId: '76561198000000000'}),
+            'GET /api/library/games': json(200, empty),
+            'GET /api/library/stats': json(200, {trend: null}),
+            'GET /api/library/steam-profile': json(200, {personaName: 'Lobo', avatarUrl: null}),
+            'GET /api/library/activity': json(200, {totalMinutes: 0, days: [], recentGames: []}),
+            'GET /api/library/games-count': json(200, {count: 1, hasSteamId: true, syncStarted: true}),
+            'GET /api/library/sync-status': () => json(200, syncStatus),
+            'GET /api/library/achievements/summary': json(200, {unlocked: 0, startedGames: 0, perfectGames: 0,
+                averageCompletion: 0, pendingGames: 0, hiddenGames: 0, closest: []}),
+        });
+        renderWithProviders(<Dashboard/>, {entries: ['/dashboard']});
+        expect(await screen.findByText(/DASHBOARD.HELLO/)).toBeTruthy();
+        expect(screen.queryByText('LIBRARY.SYNCING')).toBeNull();
+
+        syncStatus = {lastSyncStatus: 'RUNNING', lastSyncedAt: '2026-10-03T10:00:00Z'};
+        await wait(3000);
+        expect(screen.getByText('LIBRARY.SYNCING')).toBeTruthy();
+        const gamesBefore = calls('/api/library/games');
+        const changesBefore = calls('/api/library/sync-changes');
+
+        syncStatus = {lastSyncStatus: 'OK', lastSyncedAt: '2026-10-04T08:00:00Z'};
+        syncChanges = json(200, {syncedAt: '2026-10-04T08:00:00Z', startedBy: 'LOGIN', seen: false, importedGames: 0,
+            changes: [{kind: 'ADDED', appid: 1, name: 'New game', amount: 0}]});
+        await wait(3000);
+
+        expect(screen.queryByText('LIBRARY.SYNCING')).toBeNull();
+        expect(await screen.findByText('SYNC_CHANGES.ADDED:1')).toBeTruthy();
+        expect(calls('/api/library/sync-changes')).toBeGreaterThan(changesBefore);
+        expect(calls('/api/library/games')).toBeGreaterThan(gamesBefore);
+    });
+});